The research focused on enhancing the measurement accuracy through the use of non-Gaussian states has garnered increasing attention. In this study, we propose a scheme to input the coherent state mixed with photon-catalyzed squeezed vacuum state into the Mach-Zender interferometer to enhance phase measurement accuracy. The findings demonstrate that photon catalysis, particularly multi-photon catalysis, can effectively improve the phase sensitivity of parity detection and the quantum Fisher information. Moreover, the situation of photon losses in practical measurement was studied. The results indicate that external dissipation has a greater influence on phase sensitivity than the internal dissipation. Compared to input coherent state mixed with squeezed vacuum state, the utilization of coherent state mixed photon-catalyzed squeezed vacuum state, particularly the mixed multi-photon catalyzed squeezed vacuum state as input, can enhance the phase sensitivity and quantum Fisher information. Furthermore, the phase measurement accuracy can exceed the standard quantum limit, and even surpass the Heisenberg limit. This research is expected to significantly contribute to quantum precision measurement.The research focused on enhancing the measurement accuracy through the use of non-Gaussian states has garnered increasing attention. In this study, we propose a scheme to input the coherent state mixed with photon-catalyzed squeezed vacuum state into the Mach-Zender interferometer to enhance phase measurement accuracy. The findings demonstrate that photon catalysis, particularly multi-photon catalysis, can effectively improve the phase sensitivity of parity detection and the quantum Fisher information. Moreover, the situation of photon losses in practical measurement was studied. The results indicate that external dissipation has a greater influence on phase sensitivity than the internal dissipation. Compared to input coherent state mixed with squeezed vacuum state, the utilization of coherent state mixed photon-catalyzed squeezed vacuum state, particularly the mixed multi-photon catalyzed squeezed vacuum state as input, can enhance the phase sensitivity and quantum Fisher information. Furthermore, the phase measurement accuracy can exceed the standard quantum limit, and even surpass the Heisenberg limit. This research is expected to significantly contribute to quantum precision measurement.

arXiv:2403.15761Mar 23, 20241 citation

Improved linear and Kerr nonlinear phase estimation via photon addition operations

Zekun Zhao, Qingqian Kang, Shoukang Chang +4 more

Abstract The precision of quantum measurements can be effectively improved by using both photon-added non-Gaussian operations and Kerr nonlinear phase shift. Here, we employ a coherent state mixed with a photon-added squeezed vacuum state as the input to a Mach–Zehnder interferometer with parity detection, thereby achieving a significant enhancement in phase measurement precision. Our research focuses on the phase sensitivity of linear phase shift under both ideal conditions and photon loss, as well as quantum Fisher information (QFI). The results demonstrate that employing the photon addition operations can markedly enhance phase sensitivity and QFI, and under optimal conditions, the measurement precision can approach the Heisenberg limit for the linear phase shift case. In addition, we delve deeper into the scenario of replacing the linear phase shift with a Kerr nonlinear one and systematically analyze the QFI under both ideal and photon loss conditions. By comparison, it is evident that employing both the photon addition operations and the Kerr nonlinear phase shift can further significantly enhance phase measurement precision while effectively improving the system’s robustness against photon loss. These findings are instrumental in facilitating the development and practical application of quantum metrology.Abstract The precision of quantum measurements can be effectively improved by using both photon-added non-Gaussian operations and Kerr nonlinear phase shift. Here, we employ a coherent state mixed with a photon-added squeezed vacuum state as the input to a Mach–Zehnder interferometer with parity detection, thereby achieving a significant enhancement in phase measurement precision. Our research focuses on the phase sensitivity of linear phase shift under both ideal conditions and photon loss, as well as quantum Fisher information (QFI). The results demonstrate that employing the photon addition operations can markedly enhance phase sensitivity and QFI, and under optimal conditions, the measurement precision can approach the Heisenberg limit for the linear phase shift case. In addition, we delve deeper into the scenario of replacing the linear phase shift with a Kerr nonlinear one and systematically analyze the QFI under both ideal and photon loss conditions. By comparison, it is evident that employing both the photon addition operations and the Kerr nonlinear phase shift can further significantly enhance phase measurement precision while effectively improving the system’s robustness against photon loss. These findings are instrumental in facilitating the development and practical application of quantum metrology.

arXiv:2505.16123Communications in Theoretical PhysicsFeb 4, 20260 citations

Phase sensitivity via photon-subtraction operations inside Mach-Zehnder interferometer

Zhou, Qisi, Kang, Qinqian, Jiang, Tao +4 more

Based on the conventional Mach-Zehnder interferometer, we propose a metrological scheme to improve phase sensitivity. In this scheme, we use a coherent state and a squeezed vacuum state as input states, employ multi-photon-subtraction operations and make intensity-detection or homodyne-detection. We study phase sensitivity, quantum Fisher information and quantum Cramér-Rao bound under both ideal and lossy conditions. The results indicate that choosing an appropriate detection method and photon subtraction scheme can significantly enhance the phase sensitivity and robustness against photon losses. Even under lossy conditions, the multi-photon subtraction schemes can surpass the standard quantum limit. Notably, the homodyne detection method can even break through the Heisenberg limit. Moreover, increasing the number of photon-subtracted can enhance both phase sensitivity and quantum Fisher information. This research highlights the significant value of this scheme in quantum precision measurement.Based on the conventional Mach-Zehnder interferometer, we propose a metrological scheme to improve phase sensitivity. In this scheme, we use a coherent state and a squeezed vacuum state as input states, employ multi-photon-subtraction operations and make intensity-detection or homodyne-detection. We study phase sensitivity, quantum Fisher information and quantum Cramér-Rao bound under both ideal and lossy conditions. The results indicate that choosing an appropriate detection method and photon subtraction scheme can significantly enhance the phase sensitivity and robustness against photon losses. Even under lossy conditions, the multi-photon subtraction schemes can surpass the standard quantum limit. Notably, the homodyne detection method can even break through the Heisenberg limit. Moreover, increasing the number of photon-subtracted can enhance both phase sensitivity and quantum Fisher information. This research highlights the significant value of this scheme in quantum precision measurement.

arXiv:2505.04499May 7, 20250 citations

Enhanced Phase Estimation via Photon-Added Two-Mode Squeezed States and Kerr Nonlinearity

Zekun Zhao, Qingqian Kang, Teng Zhao +3 more

Quantum metrology employs quantum resources to achieve measurement precision beyond classical limits. This work investigates a Mach--Zehnder interferometer incorporating a Kerr nonlinear phase shifter, with photon-added two-mode squeezed coherent states generated via four-wave mixing as input. We demonstrate that increasing both the photon-addition order and the input resource strength systematically enhances phase sensitivity, quantum Fisher information, and the corresponding quantum Cramér--Rao bound. The proposed system not only surpasses the standard quantum limit but also approaches or exceeds the Heisenberg limit for linear phase shifts, while Kerr nonlinearity enables surpassing the super-Heisenberg limit. Furthermore, the scheme exhibits enhanced robustness against photon loss, providing a promising pathway toward practical high-precision quantum metrology applications.Quantum metrology employs quantum resources to achieve measurement precision beyond classical limits. This work investigates a Mach--Zehnder interferometer incorporating a Kerr nonlinear phase shifter, with photon-added two-mode squeezed coherent states generated via four-wave mixing as input. We demonstrate that increasing both the photon-addition order and the input resource strength systematically enhances phase sensitivity, quantum Fisher information, and the corresponding quantum Cramér--Rao bound. The proposed system not only surpasses the standard quantum limit but also approaches or exceeds the Heisenberg limit for linear phase shifts, while Kerr nonlinearity enables surpassing the super-Heisenberg limit. Furthermore, the scheme exhibits enhanced robustness against photon loss, providing a promising pathway toward practical high-precision quantum metrology applications.

quant-pharXiv:2602.00700Feb 3, 20260 citations

Improved phase sensitivity in a quantum optical interferometer based on multiphoton catalytic two-mode squeezed vacuum states

Huan Zhang, Wei Ye, Chaoping Wei +4 more

The usage of non-Gaussian states to improve the phase sensitivity of interferometers has been studied before. In this paper, we introduce the multiphoton catalysis two-mode squeezed vacuum (MC-TMSV) state as an input of the Mach-Zehnder interferometer (MZI) and study its phase sensitivity with photon-number parity measurement and the influence of photon losses. We also study the statistical properties of the MC-TMSV state in terms of the average photon number, the Wigner function, and the Mandel- $Q$ parameter. Our results show that the MC-TMSV state can exhibit stronger nonclassical characteristics, thereby making the phase sensitivity more precise with either the increase of the photon-catalyzed number or the decrease of the transmissivity. Furthermore, we also consider the effects of photon losses involving external- and internal-loss processes of the MZI, and we find that in both cases the sensitivity with the MC-TMSV state can be significantly better than that with the TMSV state under the same parameters especially in the serious photon losses and small initial squeezing regimes. We also find that the multiphoton catalysis is more sensitive to the external photon losses compared with the internal ones. Our results here can find important applications in quantum metrology.The usage of non-Gaussian states to improve the phase sensitivity of interferometers has been studied before. In this paper, we introduce the multiphoton catalysis two-mode squeezed vacuum (MC-TMSV) state as an input of the Mach-Zehnder interferometer (MZI) and study its phase sensitivity with photon-number parity measurement and the influence of photon losses. We also study the statistical properties of the MC-TMSV state in terms of the average photon number, the Wigner function, and the Mandel-$Q$ parameter. Our results show that the MC-TMSV state can exhibit stronger nonclassical characteristics, thereby making the phase sensitivity more precise with either the increase of the photon-catalyzed number or the decrease of the transmissivity. Furthermore, we also consider the effects of photon losses involving external- and internal-loss processes of the MZI, and we find that in both cases the sensitivity with the MC-TMSV state can be significantly better than that with the TMSV state under the same parameters especially in the serious photon losses and small initial squeezing regimes. We also find that the multiphoton catalysis is more sensitive to the external photon losses compared with the internal ones. Our results here can find important applications in quantum metrology.

Physical Review AJan 6, 202164 citations

Phase estimation of a Mach-Zehnder interferometer via the Laguerre excitation squeezed state

Zekun Zhao, Huan Zhang, Yibing Huang +1 more

Quantum metrology has an important role in the fields of quantum optics and quantum information processing. Here we introduce a kind of non-Gaussian state, Laguerre excitation squeezed state as inputs of traditional Mach-Zehnder interferometer to examine phase estimation in realistic case. We consider the effects of both internal and external losses on phase estimation by using quantum Fisher information and parity detection. It is shown that the external loss presents a bigger effect than the internal one. The phase sensitivity and the quantum Fisher information can be improved by increasing the photon number and even surpass the ideal phase sensitivity by two-mode squeezed vacuum in a certain region of phase shift for realistic case. Our results can find significant practical applications in quantum metrology.Quantum metrology has an important role in the fields of quantum optics and quantum information processing. Here we introduce a kind of non-Gaussian state, Laguerre excitation squeezed state as inputs of traditional Mach-Zehnder interferometer to examine phase estimation in realistic case. We consider the effects of both internal and external losses on phase estimation by using quantum Fisher information and parity detection. It is shown that the external loss presents a bigger effect than the internal one. The phase sensitivity and the quantum Fisher information can be improved by increasing the photon number and even surpass the ideal phase sensitivity by two-mode squeezed vacuum in a certain region of phase shift for realistic case. Our results can find significant practical applications in quantum metrology.

arXiv:2209.00338Optics ExpressApr 25, 20238 citations

Q

parameter. Our results show that the MC-TMSV state can exhibit stronger nonclassical characteristics, thereby making the phase sensitivity more precise with either the increase of the photon-catalyzed number or the decrease of the transmissivity. Furthermore, we also consider the effects of photon losses involving external- and internal-loss processes of the MZI, and we find that in both cases the sensitivity with the MC-TMSV state can be significantly better than that with the TMSV state under the same parameters especially in the serious photon losses and small initial squeezing regimes. We also find that the multiphoton catalysis is more sensitive to the external photon losses compared with the internal ones. Our results here can find important applications in quantum metrology.